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Chapter1 BASIC CONCEPTS 1

Chapter2 CLASSIFICATIONS OF FIRST-ORDER DIFFERENTIAL EQUATIONS 8

Chapter3 SEPARABLE FIRST-ORDER DIFFERENTIAL EQUATIONS 14

Chapter4 EXACT FIRST-ORDER DIFFERENTIAL EQUATIONS 24

Chapter5 LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS 35

Chapter6 APPLICATIONS OF FIRST-ORDER DIFFERENTIAL EQUATIONS 43

Chapter7 LINEAR DIFFERENTIAL EQUATIONS:THEORY OF SOLUTIONS 67

Chapter8 SECOND-ORDER LINEAR HOMOGENEOUS DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS 77

Chapter9 nTH-ORDER LINEAR HOMOGENEOUS DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS 83

Chapter10 THE METHOD OF UNDETERMINED COEFFICIENTS 88

Chapter11 VARIATION OF PARAMETERS 97

Chapter12 INITIAL-VALUE PROBLEMS 104

Chapter13 APPLICATIONS OF SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS 108

Chapter14 THE LAPLACE TRANSFORM 125

Chapter15 INVERSE LAPLACE TRANSFORMS 138

Chapter16 CONVOLUTIONS AND THE UNIT STEP FUNCTION 146

Chapter17 SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS BY LAPLACE TRANSFORMS 154

Chapter18 SOLUTIONS OF LINEAR SYSTEMS BY LAPLACE TRANSFORMS 161

Chapter19 MATRICES 166

Chapter20 eA? 175

Chapter21 REDUCTION OF LINEAR DIFFERENTIAL EQUATIONS TO A FIRST-ORDER SYSTEM 183

Chapter22 SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS BY MATRIX METHODS 191

Chapter23 LINEAR DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS 199

Chapter24 REGULAR SINGULAR POINTS AND THE METHOD OF FRONBNIUS 213

Chapter25 GAMMA AND BESSEL FUNCTIONS 228

Chapter26 GRAPHICAL METHODS FOR SOLVING FIRST-ORDER DIFFERENTIAL EQUATIONS 236

Chapter27 NUMERICAL METHODS FOR SOLVING FIRST-ORDER DIFFERENTIAL EQUATLONS DIFFERENTIAL EQUATIONS 254

Chapter28 NUMERICAL METHODS FOR SYSTEMS 272

Chapter29 SECOND-ORDER BOUNDARY-VALUE PROBLEME 288

Chapter30 EIGENFUNCTION EXPANSIONS 298

Appendix A LAPLACE TRANSFORMS 305

ANSWERS TO SUPPLEMENTARY PROBLEMS 311

INDEX 355